Question

A bus half ticket costs half the full fare, but the reservation charges are the same on a half ticket as on a full ticket. One reserved first class half ticket from the station A to B costs 1000. Also, two reserved first class full tickets and one reserved first class half ticket from A to B costs 4000, then the difference of the full first class fare from station A to B and the reservation charges for a ticket is​

Answer 1

Given:

A bus half ticket costs half the full fare, but the reservation charges are the same on a half ticket as on a full ticket. One reserved first-class half ticket from station A to B costs 1000. Also, two reserved first-class full tickets and one reserved first-class half ticket from A to B cost 4000

To Find:

The difference between the full first-class fare from station A to B and the reservation charges for a ticket is​

Solution:

From the given information let the value of reservation cost which is a fixed cost for all tickets be 'R', then we can say that one reserved first-class half ticket from station A to B costs 1000 can be expressed as,

(Let x be the fare excluding the reservation charges for the whole trip)

R+x/2=1000       -(1)

Now for two reserved first-class full tickets and one reserved first-class half ticket from A to B cost 4000  we  can conclude that,

2(R+x)+R+x/2=4000

Taking the value from equation 1 we have,

2(R+x) +1000=4000

R+x=1500         -(2)

Now solving equations 1 and 2 we have,

2R+x=2000 and,

R+x=1500

R=500

Now the full first-class fare costs,

R+x=1500 and we have the value of R=500, so x=1000 (which is the difference between the full first-class fare from station A to B and the reservation charges for a ticket)

Hence, the difference between the full first-class fare from station A to B and the reservation charges for a ticket is​ 1000.